Efficient use of detectors for random number generation

ABSTRACT

In an apparatus and methods of random number generation, a detector (60) receives a plurality of groups of n light pulses (50), which an attenuator (40) typically dims to single-photon intensity levels. Each of the n light pulses has a probability less than one to produce a successful detection event at its time of arrival at the detector, but the detector detects only one of the n pulses per group. This single detection per group is thus a discrete random event. This detection even can occur only during one of n fixed timeslots during which a pulse may arrive at the detector. The method of the invention converts the random event at one of n timeslots into a random integer from 1 to n. The expected arrival time of the first pulse of the group becomes a timing reference with which to start a timer (90) and define the define the timeslots electronically. When the detector electronics (70) output an electronic signal (80) at the time of a successful detection event, the apparatus of the invention&#39;s preferred embodiment stops the timer and matches that detection time with one of the n timeslots. This match produces the random integer from 1 to n. The methods of the invention help to overcome the problem of long dead times that can affect the detectors used for a preferred embodiment of the apparatus. The methods of the invention using the preferred embodiment of the apparatus also help to reduce the effects of dark counts in such detectors.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims priority under 35 USC 119(e) and theParis Convention to United States provisional application serial number60/289,591, filed May 09, 2001. The entire contents of that applicationare hereby incorporated by reference.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The invention relates to random number generators.

[0004] 2. Description of the Background

[0005] A Random Number Generator (RNG) is a variable X whose value takeson a sequence of numbers in which the probability of any particularsequence is equally likely. The idea of random number generation refersto the probability of generation of any sequence being equal.

[0006] Random numbers mean sets or sequences of numbers generated by aRNG.

[0007] Pseudo-random numbers mean any distribution or sequence ofnumbers produced by a deterministic algorithm. Conventionalsoftware-based random number generators (RNGs) produce pseudo-randomnumbers.

[0008] True-random numbers mean any distribution or sequence of numbersrelying upon randomness in physical or natural events believed toprovide random events. Thermal noise in electronics and radioactivedecay are believed to provide truly random events.

[0009] Herein, the symbol τ_(d) defines the dead time or recovery timeof a detector.

[0010] A single photon detector means a detector with a substantialprobability of detecting the existence of a single photon.

[0011] APD herein means an avalanche photodetector. An APD may be asingle photon detector.

[0012] An APD dead time, τ_(d), is a duration of time after a detectionevent during which the APD remains inactive or unable to respond fullyto light incident on the APD.

[0013] APDs can be designed to operate (detect photons) in spectralwindows spanning 850 nm, 1310 nm, and 1550 nm. Silicon, Germanium, andInGaAs APD detectors are common. R. G. Brown, K. D. Ridley, and J. G.Rarity, Appl Opt 25, 4122 (1986) and Appl Opt 26, 2383 (1987) describesan APD reverse-biased above breakdown in Geiger mode that has a deadtime τ_(d),.

[0014] Effective dead times means a duration of time after a detectionevent during which the detector fails to respond fully to incident lightdue to “after-pulse” effects.

[0015] After pulse effects in APDs occur, particularly InGaAs/InP APDssensitive at 1550 nm, due to charges trapped after a detection avalanchein an APD. After pulsing effects are described in M. Bourennane et al.,Optics Express 4, 383 (1999); A. Karlsson et al., Circuits and Devices11, 34 (1999).

[0016] Rapidly quenching the avalanche in an APD reduces the APDs deadtime. Passive avalanche quenching means quenching the avalanche in anAPD using passive electronic elements. Dead times for typical passivelyquenched APDs are 1 Us. Active quenching means quenching the avalanchesin an APD using active electronic circuits.

[0017] A gated mode reduces dark count rates in a detector, such as anAPD. The gate duty cycle in the prior art of APD usage comprises oneshort time window of the order of the pulse duration for detectionfollowed by a long time window on the order of the dead time τ_(d). SeeM. Bourennane et al., J Mod Opt 47, 563 (2000). A pulsed light source'srepetition rate 1/τ_(s), can be changed relatively easily and can beorders of magnitude larger than the detector recovery rate 1/τ_(d).Light sources that can be used in conjunction with APDs include LEDs,visible and infrared lasers, and vapor lamps. Imperfect detectors (withnon-unity detection efficiency) and channel losses can be lumped into aneffective transmission coefficient

η=η_(trans) ηdetector.   (1)

[0018] The light transmission channel may be any medium or means, suchas free space, optical fiber, or waveguide, to convey electromagneticsignals from a source to a detector. Typical detector efficienciesη_(detector) are 50-75% for silicon APDs detecting light at 600-850 nmand 10-15% for InGaAs APDs at 1550 nm.

[0019] The publication by A. Stefanov et al., at URL:http://xxx.lanl.gov/abs/quant-ph/9907006, proposes detecting weakoptical signals using single photon detectors as a method of generatingtrue random numbers. Stefanov et al. proposes a pulsed light-emittingdiode (LED) attenuated to average photon number ñ<<1, two optical pathsin fiber, and one passively quenched APD for single photon detection.The apparatus splits the signal pulse between the two optical paths, oneshort and one long, to the detector. This creates two possible arrivaltime slots at the detector, one for each path, which are assigned bitvalues 0 and 1. Only a signal from one path or the other causes adetection event, but exactly which path per pulse triggers thisdetection is a random process. By using an electronic clock and logiccircuit, the apparatus reconciles the successful detection of a signalat one time slot or the other with the transit time from source todetector, producing one bit per detection event. The Stefanov et al.proposed method alternates between an active and inactive period,τ_(total)=τ_(a)+τ_(i), where τ_(a) denotes the active period and τ_(i)the inactive, for each detection cycle. Their apparatus pulses thesource once per cycle so that a photon on the short path arrives at thebeginning of the active period. Stefanov and coworkers use an activeperiod of τ_(a)≈70 ns with photons on the split paths set to arrive atthe detector only during 10 ns time windows at either end. They use apassively quenched detector with τ_(d)≈1 μs. Stefanov and coworkers setthe inactive period to be equal to the dead time τ_(d). To synchronizethe system, the method employs a source period τ_(s) that is equal toτ_(total): the source and detector run at the same clock speed.

[0020] The present inventors calculated the RNG rate of Stefanov'smethod. Their method determines the random number generation rate. TheirPoisson-distributed photon number source with small average photonnumber n gives a rate

R=(1−e^(−η) _(n))/τ_(s)≈ηñ/τ_(total)  (2)

[0021] Stefanov and coworkers set ηñ to be ˜0.1. The random bitgeneration rate from (2) is R˜100 kHz.

[0022] P. Townsend in patent PCT/GB95/01940 (US005953421) and IEEEPhotonics Technology Letters 10, 1048 (1998), demonstrate schemes todistribute quantum signals as a cryptographic key over a kilometer ormore of optical fiber. Quantum cryptography requires a quantum channelbetween source and detector, which means a channel that does not degradethe quantum information (e.g., polarization and/or phase) encoded in thesignal pulses. For example, photo detection occurs in an activelyquenched APD without gating and with τ_(d)=50 ns. See IEEE PhotonicsTechnology Letters 10, 1048 (1998), which discloses a system wherein aphoton can arrive at the detector during two distinct time slots,corresponding to bit values 0 or 1. The pulse period c, is 2.5 ns. Thelosses and average photon number effectively give ηñ˜0.006, yielding anaverage count rate of 2.4 MHz and quantum bit rate R≈1.2 MHz.

SUMMARY OF THE INVENTION

[0023] One object of the present invention is to generate randomnumbers.

[0024] Another object of the invention is to rapidly generate randomnumbers.

[0025] Another object of the invention is to provide an apparatus andmethod that provide the random number generation rate R substantiallylarger than ¹τ_(d).

[0026] In one aspect, the invention provides a system and method forRNG, comprising a transmitter for transmitting a sequence of pulses eachhaving an intensity; a detector for detecting pulses; a transmissionchannel channeling said sequence of pulses from said transmitter to saiddetector such that said detector would detect an average of one pulseper sequence of n pulses, wherein said sequence of pulses is transmittedduring a first period of time; and means for determining a second periodfrom initiating said pulses to when said detector detects said pulse.

[0027] In another aspect, the invention provides a system and method forRNG, comprising: transmitting to a detector a sequence of pulses eachhaving an intensity such that said detector would detect an average ofone pulse per sequence of n pulses, wherein said sequence of pulses istransmitted during a first period of time; detecting a pulse in saiddetector; and determining a second period from initiating said pulses towhen said detector detects said pulse.

[0028] An embodiment of an apparatus of the present invention comprisesa pulsed source of coherent or incoherent light, an attenuator, anoptical channel, and a detector. The source produces a plurality ofsequences each of n pulses. The symbol ñ defines the average photonnumber of each pulse on arrival at the detector. The attenuator dims thelight to the single photon (or low photon number) level per pulse. Inthis context “low photon number” means ñ less than 1. The channelconveys the light pulses from source to (attenuator and from attenuatorto) detector. The single photon detector detects one pulse from eachsequence of n dim light pulses per detection cycle.

[0029] The remaining elements of the apparatus control the aboveelements and comprise a controller, detector and gating electronics, atime-interval analyzer, and a microprocessor/memory device. Acontroller/pulser/clock performs timing and operational processingfunctions, like pulsing the optical source and synchronizing the sourceand detection cycles. The controller also triggers the gatingelectronics to change the bias voltage on the detector and triggers thetime-interval analyzer to start measuring the elapsed time until a photodetection event. The circuitry of the detector and gating electronics,possibly controlled by the controller, allow for the detection of theweak light signals. The gating electronics bias the detector to set thedetection efficiency either to the maximum (detector on) or toapproximately zero (detector off), respectively. The detectorelectronics quench the electronic avalanche that is caused by asuccessful detection. The detector electronics also send an electronicoutput signal to the time-interval analyzer after a successful photodetection event in order to stop the elapsed time measurement. Atime-correlated photon counting system or other time-interval analyzermeasures the elapsed time until a successful photo detection withrespect to the start trigger (timing reference) described above. Thetime-interval analyzer converts the elapsed time into a voltage. It binsthat voltage (the measure of the arrival time) into one of n voltageranges corresponding to the n pulses. It outputs a digital or analogsignal that specifies that bin number. A microprocessor/memory deviceaccepts the output from the time-interval analyzer. It then performsstorage and computational operations on the bin numbers from successivesequences of light pulses. Electrical connections may be made betweenall electronic components for synchronizing and systematizing theelectronic elements of the random number generation apparatus.

[0030] The methods of the invention use the embodiment of the apparatussummarized above to create a random integer from a plurality ofsequences of n pulses emitted by the source. The attenuator attenuatesthe light so that each pulse of each sequence has a probability lessthan one (and ideally 1/n) to cause a successful detection. In thecurrent invention, the channel for light propagation serves as apredictable way to relay the pulses to the detector. Predictable heremeans that the user can measure the approximately stationary probabilitydistribution for photo detection of the n pulses.

[0031] In a first method, the entire time duration from the arrival atthe detector of the leading edge of the first pulse to the falling edgeof the nth pulse defines an on-period for the detector during whichphoto detections can take place. The expected arrival time (of therising edge) of the first pulse at the detector defines a timingreference, used as the trigger time for the time-interval analyzer ofthe apparatus. At or just before this time, the controller signals thegating electronics to bias the detector above breakdown, initiating thedetector on-period. The gating electronics only change the bias belowbreakdown at the expected time of the falling edge of the nth pulse,ending the on-period and initiating the off-period. During the on-periodeach of the n pulses can arrive at the detector only within a fixed timeslot, numbered 1 to n, with respect to the trigger time. For eachon-period, the detector detects only one of the n pulses, but the exactpulse that the detector detects per sequence is random. Hence, the timeslot number of the detected pulse corresponds to a random integer from 1to n. Since the detection electronics send a signal to stop thetime-interval analyzer after a successful detection, the bin number thatis output by the time interval analyzer of the apparatus is equal to thetime slot number and therefore is a random integer. In other words theapparatus transforms a measurement of the detected pulse's arrival timewith respect to the timing reference into a random integer. During theoff-period, the controller controls the gating electronics to hold thedetector's bias voltage below breakdown for a time equal to the deadtime of the detector. During this off-period the source may emit lightpulses, but the detector is off and cannot detect. When this off-periodhas elapsed, the controller synchronizes the next source pulse as thefirst pulse of a new on-period.

[0032] The cycle repeats to create the next random integer from the newsequence of n pulses. The microprocessor/memory device collects therandom integers, which may be statistically correlated and biased, andconverts a string of random integers into a string of statisticallyindependent random bits using computational operations. If the randomintegers created by successful detections are statistically independentalready, each integer represents log₂n random bits. As a result, forshort on-periods compared to the off-periods, this method can provide arandom digital number generation rate that approaches R=log₂n/τ_(d).This rate can be substantially larger than 1/τ_(d). Moreover, the gatingtechnique, which turns off the detector during the off-period, reducesthe dark count rates relative to a detector that remains biasedcontinuously.

[0033] A second method that uses a preferred embodiment of the apparatusis an adaptation of the first method. The controller in the secondmethod breaks the on-period into n on- and off-sub-periodselectronically. During the on-sub-period the controller triggers thegating electronics to turn on the detector only during the time windowsthat correspond to the expected arrival times of the n pulses. Theoff-sub-periods are the time windows between pulses, during which thegating electronics turn off the detector. Otherwise, this methodoperates like the first. This second method lowers the dark count ratefurther since the light pulse durations and therefore the on-sub-periodsmay be much shorter than the time between light pulses, given by theinverse of the source repetition rate. For short on-periods compared tooff-periods, this method can provide a random bit generation rate thatapproaches R=log₂n/τ_(d).

[0034] A third method of using the apparatus can work as an adaptationof either of the first two methods. In the first two methods the timewindow encompassing the fixed number of n pulses defines each detectionon-period. By relaxing the constraint of a fixed on-period duration, thedark count rate can be reduced and the speed of those methods can beincreased. In this third method the off-period begins immediately aftera successful detection event. The detector electronics sends a feedbackelectronic signal to the controller at the time of a successfuldetection event. Immediately after receiving that signal, the controllersends a signal to the gating electronics to lower the detector voltagebelow breakdown and initiate the off-period. This action is a departurefrom the first two methods, where the controller waits until the end ofthe nth pulse to initiate the off-period. The system now waits anoff-period equal to the dead time before the cycle begins again with asource pulse. The average on-period now has a duration that is shorterthan the previous two methods, which reduces the dark count probability.In addition, by initiating the off-period after a successful detection,this method prevents dark counts from after-pulsing. These may occur inthe first two methods since the gating electronics maintain or raise thebias voltage above breakdown before the detection avalanche has quenchedfully. For short on-periods compared to off-periods, this method canprovide a random bit generation rate that approaches R=log₂n/τ_(d).

[0035] In a fourth method using the apparatus, a single photon sourceemits one photon per detection cycle. Alternatively, a classical lightsource, such as a laser or LED, emits a single pulse per detectioncycle. The apparatus now contains additional means to split signals anddelay the split signals with respect to one another. Using these, theapparatus can split the single pulse into a superposition of n differentsub-pulses, separated in time. For example, this method uses log₂n 50:50optical fiber couplers and fiber optic delay lines. The source pulseenters the alternating system of fiber coupler—delay line—fibercoupler—delay line . . . After each fiber coupler, the signal splitsbetween the two paths in the fiber delay line, one long and one short,before the next fiber coupler. After the last delay line, an additionalfiber coupler or other beam recombination means recombines the two delaypaths. These n sub-pulses now act as the n separate pulses used in theabove three methods, and the definitions of the detector cycles followdirectly from the n sub-pulse sequences. As a result, for shorton-periods compared to off-periods, this method can provide a random bitgeneration rate that approaches R=log₂n/τ_(d).

[0036] Generally, the invention's use of random events from successivesequences of n discrete possibilities provides a novel way to producerandom numbers. Simultaneously, the invention provides a method toreduce dark count rates and to maximize efficient detector usage whenimplemented with a preferred embodiment of an apparatus that uses dimlight pulses.

BRIEF DESCRIPTION OF THE FIGURES

[0037]FIG. 1 is a schematic of an apparatus embodying the presentinvention.

[0038]FIG. 2 shows a timing diagram for a first method of using thepreferred embodiment in FIG. 1.

[0039]FIG. 3 shows a timing diagram for a second method of using thepreferred embodiment of FIG. 1;

[0040]FIG. 4 shows a timing diagram for a third method of using thepreferred embodiment of FIG. 1; and

[0041]FIG. 5 outlines a method of using an embodiment of the presentinvention that splits a single signal into n=2N signals, which impingeon a detector.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0042]FIG. 1 shows a system 1. System 1 includes photon or optical pulsesource 20, light conducting channel 30, attenuator 40, light conductingchannel 50, detector 60, detector gating electronics 70, detector output80, time correlated photon counting 90, data line 100,microprocessor/memory 110, random number output 120, control/data line130, controller/pulser/clock 140, control line 150, control line 160,control/data line 170, and control/data line 180.

[0043] Source 20 produces a plurality of sequences of n pulses, whichare plotted as source power versus time in FIGS. 2, 3, and 4 fordifferent methods of using the preferred embodiment. Source 20 mayconsist of a coherent light source or an incoherent light source. Source20 emits pulses directly or emits continuous light from which a pulseror amplitude modulator slices pulses. Channel 30 conveys photons fromsource 20 to attenuator 40. If source 20 provides sufficiently lowenough intensity pulses, attenuator 40 is not necessary. Channel 50conveys photons from attenuator 40 to detector 60. The peak power perpulse from source 20 and the optical density of attenuator 40 are suchthat attenuator 40 dims the light to the single photon (or low photonnumber) level per pulse. Each optical pulse contains an average number nof photons. Detector 60 detects one pulse from each sequence of n dimlight pulses per detection cycle. The symbol η represents the effectivetransmission coefficient, combining channel losses and detectorefficiency.

[0044] Elements 70-130 are an electronic control system for the source,detector, and attenuator. These elements also provide a processing unitto convert the detection of one of n pulses per sequence into randombits. They comprise controller 140, detector and gating electronics 70,time correlated photon counter, 90, and microprocessor/memory 110.Controller/pulser/clock controls timing of light from source 20, timingof detector gating electronics 70, timing of time correlated photoncounting 90, and timing of microprocessor/memory processing. Controllerpulser/clock 140 may be one device or distinct devices. The pulserpulses and/or forms the drive unit for source 20. The pulser may serveas the clock to synchronize the entire apparatus of the invention, orthe controller may have an independent clock locked to the repetitionrate of source 20. The controller also triggers the gating electronics70 to change the bias voltage on the detector and triggers the timecorrelated photon counting 90 to start measuring the elapsed time untila photo detection event.

[0045] In the description that follows, the term controller denotescontroller/pulser/clock 140. The circuitry of the detector and gatingelectronics, possibly controlled by controller 140, allow for thedetection of weak light signals and recovery of the detector after adetection event. Detector gating electronics 70 bias detector 60 withpreset voltages to be above or below breakdown. These biases set thedetection efficiency either to the maximum (detector on) or toapproximately zero (detector off), respectively. A successful detectionproduces a large electrical current flow, which is called the avalanche.Detector/gating electronics 70 quench the avalanche by lowering the biasvoltage below breakdown temporarily. Detector gating electronics 70 alsoconvert the avalanche current into an electronic output signal to sendto the time-interval analyzer after a successful photo detection eventin order to stop the elapsed time measurement. Time-correlated photoncounting 90 or another time-interval analyzer, possibly employing atime-to-amplitude converter and multi-channel analyzer, measures theelapsed time until a successful photo detection with respect to thestart trigger (timing reference) described above. Time-correlated photoncounting 90 converts the elapsed time into a voltage. Time-correlatedphoton counting 90 bins that voltage (the measure of the arrival time)into one of n voltage ranges corresponding to the n pulses. It outputsto microprocessor/memory 110 a digital or analog signal that specifiesthat bin number, which represents a raw random integer. “Raw” means thatthe integers may yet undergo processing to remove statisticalcorrelations between them and to remove any biases toward certainvalues.

[0046] Microprocessor/memory 110 accepts the output from thetime-correlated photon counting 90. Microprocessor/memory 110 performscomputational operations, as described below, on the bin numbers fromsuccessive sequences of light pulses. These operations createstatistically independent random bits from the raw random integers.These independent bits form the output of the RNG.

[0047] The memory device of microprocessor/memory 110 stores the raw andindependent random bits, as necessary. The memory device also outputsthe bits, for example as digital electrical signals, when queried by arequest circuit or a device external to the invention. The memory devicemay also have a continuous bit-output mode, synchronized to theapparatus clock or a clock external to the invention. In these ways thememory device may output random numbers at a rate equal to or slowerthan the overall random bit generation rate of the system. Additionalelectrical connections may be made between all electronic components forsynchronizing and systematizing the electronic elements of the randomnumber generation apparatus.

[0048] For an APD detector, the source must operate in the detector'swavelength range of sensitivity. For example, a coherent or partiallycoherent source may be a solid-state, semiconductor, dye, free electronor other laser. An 830 mn (1550 nm) semiconductor laser works well withsilicon (InGaAs/InP) APDs.

[0049] Silicon avalanche photo diode operating in Geiger mode areavailable from Perkin Elmer: (1) SPCM-AQR-1X (X goes from 2 to 6 fordecreasing value of the dark counts) is sensitive to wavelengths between400 mn and 1100 nm, with quantum efficiency near to 90% and photondetection efficiency near to 60% for the range 650-830 nm. This detectoris actively quenched and has a gating function. This detector is alsoavailable in the model SPCM-AQR-1X-FC with a fiber optic receptaclepre-aligned to the detector. (2) C30902S (or C30921 S that includes alight pipe) operates in the range between 400-1000 nm with quantumefficiency 60% for 900 rum and 77% at 830 nm. Both passive and activequenching are possible for this detector. A modification of thisdetector (NIR-enhanced) is also available for the infrared (IR) range,with quantum efficiency of 40% at 1064 nm. Another company from whichSilicon APDs are available is GE Canada Electro Optics (SPCM-100-PQ, canbe used in the wavelength range 400-1060 nm).

[0050] InGaAs APD detector used in 1310 nm and 1550 nm long, intermediaand short range application are available from Perkin Elmer (SRNBA 2.5,SRMBA 1.2, SRAA155, 622, 1.2), Fujitsu (FPD5WIKS), EG&G (C306444EJT-07and 30733), NEC (NDL 555 1PC), Epitaxx (EPM239AA). To use thesedetectors effectively for one photon counting it is necessary toconstruct circuits to realize Geiger mode, passive or active quenching,gating and eventually a cooler to reduce dark counts. See A. Karlsson etal., Circuits and Devices 11, 34 (1999). In particular the last threementioned models work efficiently at 1550 nm when cooled at −60° C. withPeltier cooling. NEC sells both Germanium and InGaAs devices such asNDL5102P and NDL5500P that can be used in the range 1000-1550nm.

[0051] Single photon sources, including those that emit exactly onephoton per pulse, may be available at visible and near-IR wavelengths inthe future. Spontaneous parametric down conversion can also be used tocreate a source of single photons. For example, amplified ˜800 nmTi:Al₂O₃ laser pulses, frequency-doubled to 400 nm, impinge on anonlinear crystal, such as BBO or LBO crystals available from FujianCastech Crystals, to create a pair of photons, the signal and idler,with some probability. In this case a second APD detector may detect theidler photon to confirm the presence of the signal photon, in which casethe signal photon may be used for RNG.

[0052] Longer wavelength sources, such as infrared lasers, microwave andmillimeter wave antennas, or novel GHz and THz emitters, must operatewith fast detectors such as bolometers, such as Si Bolometers, SiComposite Bolometers are available from Infrared Laboratories, or cooledphoto conductors, such as 2000-12000 nm IR photoconductors seriesPCL-2TE, PCI-L-2TE, PCI-2TE available from VIGO System, or cooled CCDsavailable from JYHoriba and ANDOR Technology, to be of interest in RNG .Shorter wavelength sources, whether ultraviolet lasers, harmonicallygenerated ultraviolet and x-ray pulses, synchrotrons, charged particleimpacts in metal targets, laser-excited plasmas, UV and x-ray freeelectron lasers, or other processes that generate bursts ofshort-wavelength radiation, are consistent with the methods of theinvention when used with fast, efficient detectors like the Bicrondetectors, such as BICRON Inorganic Scintillator Detectors, Si APDs, ordiamond detectors, which are in construction at CERN and in severaluniversities.

[0053] As an alternative to coherent or partially coherent sources, anincoherent source may be an ultraviolet, visible, or near-infrared LED.An LED that emits light centered at 850 nm works with the silicon APD.

[0054] Most coherent and incoherent light sources should give Poissondetection statistics in an APD used for random number generation, asdiscussed in L. Mandel and E. Wolf, Optical Coherence and QuantumOptics, Cambridge University Press, 1995, but the photon-numberdetection statistics are not critical to the methods of the invention.In a preferred embodiment of the apparatus, the source emits a stream oflight pulses, for example, at 830 nm from a Picoquant diode laser withpulse duration of less than 100 ps and pulse separation τ_(s) down to12.5 ns. The laser power is shown schematically in FIG. 2 beforeattenuation. This laser typically outputs average powers of ˜1 mW. ThePicoquant PDL800, the light source drive unit, acts as the pulser forthe laser and provides the system clock operating at the repetition rateof 1/τ_(s)=80 MHz for controller 140. FIG. 2 also shows the temporaloverlap of the pulse sequence with respect to the detector gate cycle,described below.

[0055] In a preferred embodiment a passive attenuator or attenuators(e.g., from Newport), such as neutral density filters or fixed settingvariable optical attenuators, decrease the intensity of each pulse bythe same amount. In this case, each pulse has the same average photonnumber n. The photon-number detection statistics are Poissonian, asdiscussed below. The attenuator can be placed immediately in front ofthe detector as long as it does not reradiate absorbed light into thedetector path. Alternatively, a voltage-controlled variable attenuatoroperating at the source repetition rate may prove useful to create, forexample, a sequence of n pulses such that each pulse has a probabilityof l/n to cause a detection event. In this case each of the n photons ina sequence would have a different average photon number, which would becalibrated with the detector response to give a flat probabilitydistribution for photo detections over the n pulses. A high-speedelectro-optic modulator, for example driven by a function-generated RFsignal for amplitude modulation and combined with a passive attenuator,may perform the voltage-controlled variable attenuator function.

[0056] For the preferred embodiment the channel is free space. Anotherpossibility is standard SMF-28 optical fiber. The fiber channel maycouple to pigtail fiber or fiber connectors, such as model SIFAMP2S13AA50, mounted to the source output and/or detector input in commoncommercial product configurations. Fiber coupling to the detector fromfree space can help to avoid stray late from affecting the operation ofthe detector.

[0057] In a preferred embodiment, a passively quenched silicon APD,operated in Geiger mode, detects the 830 nm light at single-photon lightlevels. APD model C30902S from EG&G/Perkin-Elmer provides detectionefficiencies of about 50%. A thermoelectric cooler stage can help toprovide temperature and operational stability near −20° C. The detectorelectronics then assure timing resolution on the order of a nanosecondand electronic output to signal a successful detection event. Inparticular, a high voltage source DC biases the detector at 250 V,roughly 20 V below breakdown. This is the low detector gate voltageshown in FIG. 2. At this bias the detector is off. In accordance withthe methods of the invention, the gating electronics—e.g., a fast risetime, TTL-controlled voltage supply—provides a transient voltage ofroughly 40V in series with the 250 V DC to bias the APD above breakdownand thus turn on the detector. When biased 20 V above breakdown, asuccessful detection event or dark count causes an avalanche current toflow through the APD. The remaining detector electronics consist, forexample, of an avalanche-current limiting resistor of ˜200 kΩ thatconnects the APD in series to a grounded ˜50 Ω load resistor in parallelwith an amplifier stage. The limiting resistor quenches the avalanche.The amplifier stage sends the amplified output to a discriminator, whichclearly identifies the avalanche events. The discriminator then outputsa TTL pulse to controller 140 and time-interval analyzer to indicatethese successful events to the system. Commercial amplifier anddiscriminator systems are available, for example, fromOrtec/Perkin-Elmer.

[0058] Controller 140 provides several control functions for the system,as mentioned above. In the preferred embodiment a Xilinx FPGA unit,synchronized with the Picoquant PDL800 light source drive unit, formscontroller 140. A combination of standard analog and digital chips couldcombine to form alternative controllers. A circuit designer can alsocreate an application-specific printed circuit board layout, designed toperform all control functions.

[0059] A time-to-amplitude conversion circuit and a multi-channelanalyzer combine to form a time-interval analyzer or counting device.Commercial units are available from Ortec/Perkin-Elmer, Becker & Hickl,and Edinburgh Electronics. The counting system receives standard TTLinputs to start and stop the counting process. The counting system sendsTTL outputs to controller 140 and microprocessor/memory device asrequired. An embedded system or PC with an analog and/or digital 1/0board can function as the microprocessor/memory device. Alternatively,the Xilinx FGPA unit serves as both controller and microprocessor/memorydevice to centralize system functions. Consistent with the methods ofthe invention, the combined controller and microprocessor/memory devicemust have a logical program to send timing signals to the gatingelectronics and time-interval analyzer at the appropriate times, collectand process output from the detector electronics and time-intervalanalyzer, and output random bits. The timing resolution and jitter ofthe electronics are sufficient to produce random numbers according tothe examples given below for using the preferred embodiment of theapparatus.

[0060] The methods of the invention use the preferred embodiment of theapparatus to create a random integer from a plurality of sequences of npulses emitted by the source. The attenuator attenuates the light sothat each pulse of each sequence has a probability less than one tocause a successful detection. The methods dictate that the sum over ndetection probabilities in each sequence approaches one, meaning onerandom photo detection will occur for each sequence. In the preferredembodiment, the channel for light propagation serves simply as apredictable means to relay the pulses to the detector. This means thatthe probability distribution for photo detection per sequence over the npulses should be stationary and measurable. In this case the detectionprobabilities for the n discrete events per sequence form a discreteprobability distribution. Thus, the methods using the preferredembodiment of the apparatus both create the discrete distribution and“sample” random integers from it.

[0061] The Poisson detection statistics of a passive attenuation schemeprovide a sufficient probability distribution. The sum over theprobabilities will approach one for certain minimum values of ñ thatdepend on n, as seen below. However, if a fast voltage-controlledattenuator sculpts the peak power of the n pulses to make a flatdistribution with detection probability 1/n for each pulse of thesequence, then the methods of the invention require less processing toremove bias. The sum over the n probabilities of the flat distributionis unity by construction, guaranteeing a photo detection event in eachsequence.

[0062] A source-detector timing cycle for an example of the first methodof using the preferred embodiment is shown in FIG. 2.

[0063]FIG. 2 shows pulse verses time schematic 200 including pulsestream 210 versus time, detector gate voltage 220 versus time, andlegend 230. Pulse stream 210 represents optical pulses generated bysource 20 of FIG. 1. Pulses 1 . . . n, illustrated as all pulses betweenpulse 1 (element 240) and pulse n (element 250) have a duration equal toduration 260 of gate on time of detector gate voltage 220. Source 20'spulses 205 show the pulses at the beginning of a subsequent gatingcycle. In the method corresponding to FIG. 2, detector 60 is set to havea gated on-period τ_(on) and off-period τ_(off) within each totaldetector period τ_(A).

[0064]FIG. 2 shows a typical, gate voltage pattern 220 versus time. Atthe high gate voltage, say 20 V above breakdown, the detector can detectphotons. At the low voltage, say 20 V below breakdown, the detector doesnot respond to incident light.

[0065] In one detection cycle the time duration from the arrival at thedetector of the leading edge of the first pulse in the sequence to thefalling edge of the nth pulse defines τ_(on)>nτ_(s). The expectedarrival time (of the rising edge) of the first pulse at the detectordefines a timing reference, used as the trigger time to start thetime-interval analyzer. At or just before this time, controller 140signals gating electronics 70 to bias detector 60 above breakdown,initiating the detector on-period. Controller 140 only signals gatingelectronics 70 to change the bias below breakdown at the expected timenτ_(s) of the falling edge of the nth pulse with respect to the trigger,initiating the off-period. During the on-period each of the n pulses canarrive at detector 60 only within fixed time slots numbered 1 to n inFIG. 2, with respect to the trigger time. For each on-period, detector60 detects only one of the n pulses, but the exact pulse that detector60 detects per sequence is a random event.

[0066] A dark count may occur when the detector is on. A dark count thatoccurs within the on-period but outside of one of the n time slots ruinsthat sequence of pulses for random number generation: the time-intervalanalyzer will not bin such an event into one of the n voltage rangesthat correspond tmo the light pulse timeslots. A dark count during oneof the n timeslots would mimic a photo detection event. The dark countsare also random events, but they have a different probabilitydistribution than the photodetections and are best avoided by keepingTon <<cd Once detector 60 detects a photon in a slot nd <n, the APD isrelatively unresponsive for the remainder of ton if Ton c<<τ_(d) and ifafter-pulsing is not a problem. Since this method does not requiregating electronics 70 to lower the bias voltage below breakdown untilafter the nth pulse arrives, a dark count or after-pulse during one ofthe time slots after a photodetection event within the same detectioncycle is unlikely. Regardless, the time-interval analyzer only registersthe first event per n pulse sequence. A photodetection event can onlyoccur during one of the n timeslots defined by the source pulses. Thus,the timeslot number of the detected pulse corresponds to a randominteger from 1 to n (with information equal to log₂n bits). Sincedetection electronics 70 converts the avalanche into a signal that stopstime correlated photon counting 90 after a successful detection, the binnumber that is output by time correlated photon counting 90 equals theraw random integer given by the time slot number.

[0067] During the off-period, controller 140 controls gating electronics70 to hold detector 60's bias voltage below breakdown for a timeτ_(off)>τ_(d). The off-period allows the detector electronics to quenchthe avalanche and return the detector to full efficiency. The off-periodalso reduces the dark count rate compared to a detector that iscontinuously (DC) biased above breakdown. When this off-period haselapsed, detector 60 will detect properly when biased above breakdownagain. Controller 140 resets the time correlated photon counting 90during the off-period. Controller 140 then synchronizes the next sourcepulse as the first pulse of a new on-period, as seen in the right handside of FIG. 2. Synchronization of the detector period with source 20requires τ_(off) to be slightly different than τ_(d) so that thedetector cycle remains locked to the source clock. The cycle repeats tocreate the next random integer from the new sequence of n pulses. Thus,

t_(A)>nτ_(s)+τ_(d).   (3)

[0068] As an example, for n=8, nτ_(s)=100 ns and τ_(d)=1 μs, the totaldetector period would be τ_(A)>1.1 μs.

[0069] This method of using the preferred embodiment dictates that theaverage photon number ñ of each of the n pulses, given the efficiency η,creates a probability that approaches unity to have one detection eventper sequence. From Poisson statistics, ignoring dark counts, theprobability of one photo detection in n consecutive pulses (orequivalently time slots) if n is the same for each pulse is:

P=1−exp[−nñη]1.   (4)

[0070] This expression assumes that only one pulse per sequence cancause a detection event. A small probability exists that a detectionevent will not occur during the time τ_(on), in which case that sequenceof n pulses does not produce a random number. With ηñ=0.56 and n=8,P=1−exp[−nñη]≈0.99. However, the probability to detect a photon in anysingle pulse per on-period declines as the pulse number increases. Forexample, if the probability to detect a photon in the mth pulse is givenby P(m), then P(1)=1−exp[−ñη], P(2)=P(1)*(1−P(1)),P(3)=P(1)*(1−P(1)−P(2)), . . . In other words, P(m) is given byexp[−(m−1)ñη]−exp[−mñη]. (By definition, the sum P=P(1)+P(2)+. . . +P(n)gives equation (4).) Such a scheme requires the RNG to remove bias fromthe detection-generated bits, as described below. In principle, we candistribute the photon detection probability per time slot evenly overthe n pulses (e.g., to reduce the computational effort needed to removebias from the bit stream). This could be done, for example, byprogramming a voltage-controlled attenuator with a function generator tovary n as a function of m in such a way to make P(m)=1/n for a set of npulses. To implement this, the bandwidth of such a variable attenuatorsystem should provide fast enough switching times to keep up with thesource repetition rate 1τ_(s). Controller 140 would then synchronize thefunction generator to the source-detector system.

[0071] From equation (3), ignoring any need for removing bias for themoment, the random bit production rate is roughly

R=log₂n/τ_(A)  (5)

[0072] with a limit of R=log₂n/τd for nτ_(s), <<τ_(d). For n=8 and τ_(A)=1.1 μs, equation (5) gives a rate of 2.7 MHz.

[0073] The produced raw bits, as a stream, may contain correlations, aswell as biases toward specific values. For example, correlations ariseif the probability to detect a pulse in the current sequence depends onthe previous successful detection event(s). Bias arises if the detectionprobability in each of the time slots m is not uniform. The need toremove correlation and bias is well known in random number generation.See for example, see J. von Neumann, Monte Carlo Method, Applied MathSeries, 12, U.S. National Bureau of Standards, Wash. D.C., 36-38(1951);P. Elias, Annals Of Math Stats 43, 865 (1972); Y. Peres, Annals of Stats20, 590 (1992). Elias gives a method to remove correlations in a singlebit generator that extends to multi-bit generators. Elias' method doesnot reduce the number of bits and works on the random integers asproduced. Von Neumann's method allows bias removal on uncorrelated bitsof a single bit generator by selecting out only the 0-1 and 1-0 pairsand mapping them onto 1 and 0, respectively. Peres gives an iterativeprocedure based on Von Neumann's method that can approach the fullentropy of the bit stream. Practically, these mathematical proceduresimply that bits do not have to be thrown out while removing correlationand bias if the entropy of the string approaches one per bit. As aresult, the random bit rate R can approach equation (5) if thecomputational time to remove correlation and bias is negligible comparedto the dead time.

[0074] Microprocessor/memory 110 collects the random integers andconverts the raw string of random integers from photo detection eventsinto a final string of statistically independent random bits using theabove or similar computational methods. If the raw random integerscreated by successful detections are statistically independent already,each integer represents log₂n/ρ_(d) final random bits. As a result, forshort on-periods compared to the off-periods, this method can provide arandom number generation rate that approaches R=log₂n/τ_(d). This ratecan be substantially larger than 1/τ_(d). For raw strings withcorrelations and/or bias, if the computational procedures to createindependent bits are fast compared to the dead time and reduce thenumber of bits by the factor h (roughly the entropy per bit), the randomnumber generation rate can approach R=hlog₂n/τ_(d).

[0075] In a second method of using the embodiment of the apparatus,controller 140 and gating electronics 70 divide detector 60's on-periodduration Ton of the first method into a sequence of n on-sub-periods ofduration τ_(a) and n off-sub-periods of duration τ₁:τon=n(τ_(a)+τ₁)>nτ_(s). Detector 60 can detect photons or record darkcounts during the on-sub-periods and cannot detect light or record darkcounts during the off-sub-periods. FIG. 3 shows this rapid gating methodschematically, where the source pulses and corresponding on-sub-periodsare labeled 1 to n.

[0076]FIG. 3 shows pulses verses time schematic 300 including pulsestream 310 versus time, detector gate voltage 320 versus time, andlegend 330. Pulse stream 310 represents optical pulses generated bysource 20 of FIG. 1. Pulses 1 . . . n, illustrated as all pulses betweenpulse 1 (element 340) and pulse n (element 350) each have a durationequal to, or more practically, slightly shorter than, duration 360 ofgate voltage pulses of detector gate voltage 320. Source 20's pulses 305show the pulses at the beginning of a subsequent gating cycle. Duration360 shows the duration of gating of voltage on detector 60. With respectto the pulse durations and duration 360, the point is that there may besmall time jitterings which can introduce bias in the random numbergeneration. Therefore, it is not realistic, in practice, to set the twodurations to be strictly equal to each other.

[0077] During the mth on-sub-period controller 140 triggers gatingelectronics 70 to turn on detector 60 only during the time window thatcorresponds to the expected arrival time of the mth pulse. Controller140 should set the detector on-sub-period duration to be longer than thelight pulse duration (to allow for electronic bandwidth constraints andtiming jitter) but shorter than the time between pulses. Theoff-sub-periods are the time windows between the n pulses of thesequence when photons used for random number generation cannot arrive atdetector 60. Controller 140 and gating electronics 70 turn off detector60. Controller 140 maintains synchronization of the pulsed light sourcewith these detector on- and off-sub-periods. To implement this method,the response of the APD detector coupled to its electronics must followthe changes in the applied bias voltage on the time scale τ_(a).Controller 140 and time correlated photon counting 90 can now correlatethe n bins of time correlated photon counting 90 with the n possibledetection time slots directly using the electrical signals that triggerthe n gating on-sub-periods. In contrast, in the first method the n binscorrelate with the expected arrival time windows of the n light pulses.

[0078] In other respects this second method operates like the first.Since controller 140 sets the off-period duration τ_(off) equal to thedead time τ_(d) as in the first method, the total detector period τ_(B)is now

τ_(B)=τ_(on)+τ_(off)>n(τ_(a)+τ₁)+τ_(d).   (6)

[0079] The second method lowers the dark count rate compared to thefirst method for the same τ_(on) and τ_(d) by the ratio τ_(a)/τ_(s)since the light pulse durations and therefore the on-sub-periods τ_(a)may be much shorter than τ_(s). For example, specific values for thesame source parameters as above might be τ_(s)=5 ns, τ₁=15 ns,τ_(s)=τ_(a)+τ₁=20 ns, n=8, and τ_(d)=1 ps. The rapid gating would reducethe dark counts by the ratio τ_(a)/τ_(s)=1/4 compared to the firstmethod example with τ_(on)=160 ns. Ideally, the total probability todetect a photon during Ton is close to unity, as explained above.Controller 140 again precisely synchronizes the source and detector sothat the next detection cycle after a time τ_(off) corresponds to thesource clock. Then, the random bit production rate is roughly

R=log₂n/τ_(B)=log₂n/[n(τ_(a)+τ₁)+τ_(d)]  (7)

[0080] from equation (6) with a limit of R=log₂n/τ_(d)forn(τ_(a)+τ₁)<<τ_(d).

[0081] In the above two methods of using the preferred embodiment, thedetector cycle is synchronous in the sense that controller 140 and gateelectronics 70 always gate detector 60 in the same way. The timeduration τ_(on)+τ_(off) defines this periodicity. Detector 60'soff-period always starts at the fixed time after the detector on-periodbegins, regardless of when a detection event takes place. The detectorthen remains off for a fixed time τ_(off).

[0082] A third method of using the preferred embodiment of the apparatuscan improve the performance of the invention. This third method, whichcan be adapted from either of the gating schemes of the previous twomethods, constitutes an asynchronous detector cycle. This means that adetection on-cycle of fixed duration is not required before gatingelectronics 70 lower the detector bias below breakdown for durationτoff=τ_(d). Instead, detector 60's electronics sends positive logicalsignals both to time correlated photon counting 90 and controller 140after a successful detection event. Controller 140 then triggers gatingelectronics 70 to lower the detector bias immediately, initiating theoff-period. Alternatively, detector electronics automatically triggergating electronics 70 directly to lower the bias voltage below breakdownafter a photodetection and simultaneously signal controller 140.

[0083] The possibilities for each n-pulse sequence of interest are: (a)a detection event occurs at timeslot n_(d)<n, or (b) the time durationnτ_(s) relative to the timing reference elapses, corresponding to thearrival of the n pulses without a detection event. Possibility (b) onlyoccurs with small probability, in which case the gating electronicslower the bias voltage as in the first two methods. The source, asbefore, produces pulses at the fixed repetition rate 1/τ_(s). For thismethod, an example of detection events in the second time slot of onedetector on-period and the (n-1)st timeslot of the subsequent on-periodis given in FIG. 4. This example uses the rapid gating scheme of thesecond method. The key point is the following.

[0084]FIG. 4 shows pulse verses time schematic 400 including pulsestream 410 versus time, detector gate voltage 420 versus time, andlegend 430. Pulse stream 410 represents optical pulses generated bysource 20 of FIG. 1. Pulses 1 . . . n, illustrated as all pulses betweenpulse 1 (element 440) and pulse n (element 450). Source 20's pulses 405show the pulses at the beginning of a subsequent gating cycle. In themethod corresponding to FIG. 4, detector voltage pulses of a cycle ceaseafter less than n pulses, as shown by last pulse 435 of a cycle, whendetector 60 detects a pulse.

[0085] By initiating the off-period after a successful detection, thismethod prevents dark counts owing to after-pulsing. These may occur inthe first two methods since the gating electronics maintain or raise thebias voltage above breakdown before the detection avalanche has quenchedfully. As a result, this method is especially useful for InGaAs APDswith 1550 nm light sources. InGaAs APDs are available fromEG&G/Perkin-Elmer.

[0086] The average on-period now has a duration that is shorter than inthe previous two methods approximately by the ratio of the averagedetected pulse number divided by n, which reduces the average dark countprobability. Specifically, the average on-period duration is now˜<m>τ_(s) instead of nτ_(s), where <m> is the average pulse detected ineach n-pulse sequence. For example, for uniform probability of detectionof the mth pulse, P(m)=1/n, the average detection occurs for<m>=(n+1)/2. In a rapid gating scheme like the second method,<mn>τ_(s)=(n+1)(τ_(a)+τ₁)/2 gives an average bit rate:

R≈log₂n/[(n+1)(τ_(a)+τ₁)/2+τ_(d)].   (A)

[0087] (One finds the rate for the Poisson statistics of equation (4) bycalculating <m>=(1−e^(−nη))⁻¹−n(e^(nnη)−1)⁻¹<n.) In general, asynchronous detector cycle adapted from the first method above mayproduce bits at a rate

log₂n/τ_(d)>R >log₂n/(nτ_(s)+τ_(d))   (8)

[0088] while an asynchronous cycle adapted from the second method mayproduce bits at a rate

log₂n/τ_(d)>R >log₂n/[n(τ_(a)+τ₁I)+τ_(d)]  (9)

[0089] from equation (A). For short on-periods compared to off-periods,this method can provide a random bit generation rate that approachesR=log₂n/τ_(d).

[0090] A fourth method uses a variation of the apparatus shown inFIG. 1. The apparatus now contains additional means to split a pulse intime and/or space and delay the split signals with respect to oneanother. A single-photon source or an attenuated classical light source,as above, emits one pulse. For example, the additional elements splitthe single pulse into n sub-pulses that each travel along a differentpath in space and time to the detector. In the single photon case, thefiber couplers, delay lines, and additional channel elements relay thesignal to the detector with as little degradation of the optical signalas possible. For light from the classical source, the probabilitydistribution of photo detections can be adjusted with the attenuator, asabove.

[0091] The single pulse from the source becomes a superposition of ndifferent sub-pulses, separated in time on arrival at the detector. FIG.5 shows a schematic representation of an apparatus for such a process.

[0092]FIG. 5 shows device 500 including signal pulse channel 505, splitsignal delay loops 510, 515, 525 each of which is coupled to a non-delaychannel via for example fiber coupler 520. Non-delayed and delayedpulses recombine and impinge detector 535 via channel 530.

[0093] For an example of use of device 500 shown in FIG. 5, take n to bea power of 2. A total of 1+log₂n 50:50 optical fiber couplers 520 andlog₂n fiber optic delay loops 510, 515, 525 exist. The source pulseenters the alternating system of fiber coupler—delay loop—fibercoupler—delay loop . . . After each fiber coupler 520, the signal splitsbetween the two paths in the fiber delay line, one long and one short,before the next fiber coupler. After the last delay line, an additionalfiber coupler or other beam recombination means recombines the two delaypaths. These n sub-pulses at the detector now act as the n separatepulses used in the above three methods. In other respects, this methodfunctions as one of the three methods above. One advantage to thistemporal pulse splitting scheme is the reduction of physical resourcescompared to spatial beam splitting techniques. Using fiber, for example,the ˜1+2log₂n fiber devices can generate n sub-pulses and thus an N-bitrandom number with one detector, as described schematically in FIG. 5.(Alternatively, for a spatial beam splitting apparatus in free space,standard (spatial) beam splitters and n different detectors replace thefiber devices and single detector as additional means to split and delaypulses.) The sensitivity requirement of the electronic system is then atiming resolution sufficient to distinguish the time slots thatrepresent the information, as in the other methods of using thepreferred embodiment. As a result, for short on-periods compared tooff-periods, this method can provide a random bit generation rate thatapproaches R=log₂n/τ_(d).

[0094] While the methods above envision specific implementations, thebasic principle of the invention to translate a sequence of n discretetypes of photo detection events into a multi-bit random number canincrease the random number generation rate in other settings, especiallyfor detectors with long dead times. For example, a detector with (long)effective dead times can record the timing information of continuoussignal sources or a continuous random process like dark counts withrespect to an external clock to form random numbers. Controller 140 maythen provide electronic clocking for the detector on- and off-periods,and the continuous signal will translate into discrete data values afterbinning by the time interval counting electronics.

[0095] The asynchronous detection cycle, where the gating electronicsshut off a detector for a duration slightly shorter than the dead timeright after a detection event, applies to a 10 general scheme where thephoton time of arrival maps onto a random number. In addition, for thefirst and second methods above and other possible methods to useembodiments of the invention, subsequent detection events in the sameon-period T_(on), assumed to be unlikely, may occur. These subsequentdetection events before the τ_(off) period begins may generate randomnumbers if considered, possibly increasing the RNG's rate further.

[0096] Various alternatives are available for a clock as well. Insteadof having the external clock that pulses the source serve as a masterclock for the detector directly, the light source itself can serve thispurpose. For example, a beam splitter can split off a clock laser pulsefrom the main signal pulse before attenuation, detect that clock pulsein a PIN photo diode, and convert the diode signal into an electricaltrigger through controller 140. In this alternative way controller 140synchronizes the detector to the source, which is useful for longerchannels. Additionally, the method and apparatus use the same channel ormedium for calibration and synchronization as random number generation,for example by multiplexing clock and/or calibration light signals withthe pulses that produce random numbers. See also U.S. Pat. No. 5,675,648to Townsend.

[0097] While the summary and description of the preferred embodimenthave focused on photons, the present invention applies to any type ofsignals and can be easily extended to time slot information from randomevents in multiple detector RNG schemes.

[0098] While only certain features of the present invention have beenoutlined and described herein, many modifications and variations will beapparent to those skilled in the art. Therefore, the claims appendedhereto are intended to cover all such modifications and variations thatfall within the broad scope of the invention.

We claim:
 1. A method for RNG, comprising: transmitting to a detector asequence of pulses each having an intensity such that said detectorwould detect an average of one pulse per sequence of n pulses, whereinsaid sequence of pulses is transmitted during a first period of time;detecting a pulse in said detector; and determining a second period fromwhen initiating said pulses to when said detector detects said pulse. 2.The method of claim 1 further comprising determining a ratio of saidsecond period to said first period.
 3. The method of claim 1 furthercomprising associating an integer between 1 and n with said secondperiod.
 4. The method of claim 1 further comprising gating said detectorso that said detector is capable of detecting said pulses during saidfirst period.
 5. The method of claim I further comprising gating saiddetector so that said detector is not capable of detecting said pulsesfor a period at least as long as a dead time of said detectorimmediately after said first period.
 6. The method of claim 1 whereinsaid detector is gated so that it is not capable of detecting saidpulses for a period at least as long as a dead time of said detectorbeginning immediately after said step of detecting.
 7. The method ofclaim 1 further comprising gating said detector so that said detector isonly capable of detecting any one pulse of said sequence of pulsesduring a time when said pulse is anticipated to arrive in said detector.8. The method of claim 7 wherein said detector is gated so that it isnot capable of detecting said pulses for a period at least as long as adead time of said detector beginning immediately after said step ofdetecting.
 9. The method of claim I wherein said detector is an APD. 10.The method of claim 9 wherein said detector is gated by applying avoltage either below or above a threshold voltage for avalanche in saiddetector.
 11. The method of claim 1 further comprising splitting eachpulse into more than one sub pulse and time delaying at one sub pulserelative to one other sub pulse.
 12. The method of claim 1 comprisingRNG at a rate approaching log base 2 of the quantity n divided by thedetector dead time.
 13. The method of claim 12 where said rate is atleast 25 percent.
 14. The method of claim 12 wherein said rate is atleast 50 percent.
 15. The method of claim 12 wherein said rate is atleast 75 percent.
 16. The method of claim 1 further comprisingdetermining in which of a sequence of time intervals said detectingoccurs.
 17. The method of claim 16 wherein a sum of said n timeintervals substantially equals said first period of time.
 18. A systemfor RNG, comprising: a transmitter for transmitting a sequence of pulseseach having an intensity; a detector for detecting pulses; atransmission channel channeling said sequence of pulses from saidtransmitter to said detector such that said detector would detect anaverage of one pulse per sequence of n pulses, wherein said sequence ofpulses is transmitted during a first period of time; and means fordetermining a second period from when initiating said pulses to whensaid detector detects said pulse.
 19. The system of claim 18 furthercomprising means for determining a ratio of said second period to saidfirst period.
 20. The system of claim 18 further comprising means forassociating an integer between 1 and n with said second period.
 21. Thesystem of claim 18 further comprising means for gating said detector sothat said detector is capable of detecting said pulses during said firstperiod.
 22. The system of claim 18 further comprising means for gatingsaid detector so that said detector is not capable of detecting saidpulses for a period at least as long as a dead time of said detectorimmediately after said first period.
 23. The system of claim 18 whereinsaid detector is gated so that it is not capable of detecting saidpulses for a period at least as long as a dead time of said detectorbeginning immediately after said step of detecting.
 24. The system ofclaim 18 further comprising means for gating said detector so that saiddetector is only capable of detecting any one pulse of said sequence ofpulses during a time when said pulse is anticipated to arrive in saiddetector.
 25. The system of claim 24 wherein said detector is gated sothat it is not capable of detecting said pulses for a period at least aslong as a dead time of said detector beginning immediately after saidstep of detecting.
 26. The system of claim 18 wherein said detector isan APD.
 27. The system of claim 26 wherein said detector is gated byapplying a voltage either below or above a threshold voltage foravalanche in said detector.
 28. The system of claim 18 furthercomprising means for splitting each pulse into more than one sub pulseand time delaying at one sub pulse relative to one other sub pulse. 29.The system of claim 18 designed to provide RNG at a rate approaching logbase 2 of the quantity n divided by the detector dead time.
 30. Themethod of claim 29 where said rate is at least 25 percent.
 31. Themethod of claim 30 wherein said rate is at least 50 percent.
 30. Themethod of claim 29 wherein said rate is at least 75 percent.
 31. Thesystem of claim 18 further comprising means for determining in which ofa sequence of n time intervals said detecting occurs.
 32. The system ofclaim 31 wherein a sum of said n time intervals substantially equalssaid first period of time.
 33. An apparatus for providing random numbergeneration at a rate R substantially larger than 1/τ_(d), comprising, asource of light providing low photon number; a single photon detector; achannel to convey the photons from the source to the detector; means toattenuate the light, if necessary; means for gating a detector, ifdesired; means for synchronizing the source, detector, and othercomponents of the random number generation apparatus; means fordistinguishing between detector events that occur during a number ofpossible different time slots over a detection cycle; means ofcorrelating photon receipt time in the detector with a timing referencefor random number generation; means for recording, processing, andoutputting random numbers.